Probability of a Girl Assuming that boys and girls are equally likely, find the probability of a couple having a boy when their third child is born, given that the first two children were both girls.

Suppose there are n independent trials of an experiment with k>3 mutually exclusive outcomes, where pi represents the probability of observing the ith outcome. The ____________ for each possible outcome are given by Ei = __.

The spinner below has 6 equal regions. Find the probability of landing on yellow for the first spin and not landing on yellow on the second spin.

The spinner below has 6 equal colored regions numbered 1-6. Find the probability of stopping on yellow for the first spin, stopping on an even number on the second spin, and stopping on blue or red on the third spin.

Same Birthdays If 25 people are randomly selected, find the probability that no 2 of them have the same birthday. Ignore leap years.

Births in the United States In the United States, the true probability of a baby being a boy is 0.512 (based on the data available at this writing). For a family having three children, find the following.

b. The probability that all three children are boys.

Births in the United States In the United States, the true probability of a baby being a boy is 0.512 (based on the data available at this writing). For a family having three children, find the following.

d. The probability that at least one of the children is a girl.

Alarm Clock Life Hack Each of us must sometimes wake up early for something really important, such as a final exam, job interview, or an early flight. (Professional golfer Jim Furyk was disqualified from a tournament when his cellphone lost power and he overslept.) Assume that a battery-powered alarm clock has a 0.005 probability of failure, a smartphone alarm clock has a 0.052 probability of failure, and an electric alarm clock has a 0.001 probability of failure.

b. If you use a battery-powered alarm clock and a smartphone alarm clock, what is the probability that they both fail? What is the probability that both of them do not fail?

In Exercises 29 and 30, find the probabilities and indicate when the “5% guideline for cumbersome calculations” is used.

Medical Helicopters In a study of helicopter usage and patient survival, results were obtained from 47,637 patients transported by helicopter and 111,874 patients transported by ground (based on data from “Association Between Helicopter vs Ground Emergency Medical Services and Survival for Adults with Major Trauma,” by Galvagno et al., Journal of the American Medical Association, Vol. 307, No. 15).

b. If 5 of the subjects in the study are randomly selected without replacement, what is the probability that all of them were transported by helicopter?